Engineering Rome

The Enduring Arch

jacoby9 jacoby9 Sep 16, 2013

Design Factors Learned from Roman Arched Bridges Both Past and Present

Figure 1: Ponte Garibaldi serving as both pedestrian walkway and traffic arterial ( Photo by: Self, 2013)


The arch made its first appearance in structural design in the second millennium BC via the Mesopotamian’s. However, it wasn’t until the Romans came along in 753 BC, after the Second Punic War, that the arch began to blossom in structural design (Robertson, 1943). The Romans used the arch for many things including but not limited to the aqueducts, sewage (Cloaca Maxima), buildings, and of course, bridges. The famous semicircular arches of the Ponte Fabricio, built in 62 BC, are still standing today after 2,073 years, showing the resilience of this simple architectural and structural element. The Ponte Fabricio is just one of the many arched bridges, which span the great Tiber River today and still function as needed by Rome. There are other modern bridges, such as the Ponte Garibaldi, which utilize the arch shape as well. The many arched bridges currently standing in Rome illustrate the fact that design of a span is a combination of many things, and that, Roman engineers past and present have both succeeded and failed in accommodating multiple design factors.

Design Factors

Structural Design

One of the most obvious services a bridge needed to provide for the Romans was to function as a structure in itself. That is to say, a bridge should provide the structural stability necessary to prevent any type of failure from occurring after construction. Romans didn’t have the advantage of modern construction technology at their hands as they lacked any sophisticated form of structural reinforcement (e.g., steel rebar). Reinforced concrete technology wasn’t patented until just after the middle of the nineteenth century, 1867, when Joseph Monier patented a design for reinforced garden tubs, beams, and posts (Schaeffer, 1992). Masonry arches, however, function because of their ability to absorb massive amounts of compressive force, which the Romans took advantage of religiously. The term masonry encompasses essentially all of the materials the Romans used for construction, which is discussed later.

Structural Analysis: Ponte Fabricio vs. Ponte Garibaldi

A good example of how the function of structural stability can be accomplished multiple ways is illustrated below as a comparison between the Ponte Fabricio and Ponte Garibaldi is made.

Ponte Fabricio

Figure 2: The Ponte Fabricio connecting to Tiber Island from Campus Martius (Photo by: Self, 2013)

The following analysis was used assuming the dimensions listed below in Table 1 via site visit:

Table 1: Ponte Fabricio Values

Height (m.) 14.5
Width (m.) 5.5
Arch Width (m.) 24.5
Span-to-Height Ratio 1.7

Using the values from Table 1, a thrust analysis was performed by calculating the reactions at the base of the arch. In this example, the Ponte Fabricio is considered as a three-hinged arch due to the fact that no steel reinforcing exists in the structure and the weight of the masonry structure above the arch will cause tension at the keystone region. Because masonry is weak in tension and no reinforcing exists, fixity cannot occur at this location and so, a model can be made which ignores moment at that location. As for the base, where the arch meets the abutments, again no reinforcement exists, and continuing settlement of the ground below the arch due to located weight at the base causes the connection between arch and abutment to behave like a pin. Because of this, three hinges exist: two at the base and one at the keystone.

The other assumption made upon analysis was that the density of the masonry materials used to construct the bridge was 150 lb/ft^3 (assuming that the density of Roman concrete and tuff was similar to that of Portland Cement Concrete), and although the bridge has two tapering sides from the center span, for calculation purposes, the Ponte Fabricio was treated as flat. The arches were treated as semi-circular with a radius of 24.5 meters each. Taking into account the void area of the arch, the distributed load weight above each arch was calculated to be approximately 3,500 kips. This corresponds to thrust forces in the y-direction of 1,750 kips at each arch support and a magnitude of 1,750 kips in the positive x-direction for the left hinge and negative x-direction for the right hinge. It’s important to note that the forces in the x and y-directions are the same magnitude because of the geometry of the semi-circular three-hinged arch. Same magnitudes occur because when a cut is made at the apex hinge, summing moments about that point creates equal lever arms between the two reaction forces at the base. For static analysis to be valid, the force must be equal in magnitude.

As can be seen from the analysis above, the immense self-weight of the bridge causes the two arches to be placed under compression. Masonry arches perform well under compressive stress, fair under shear stress, and poor under tension. It makes sense that in our analysis, the reactions at the base of the bridge show that the arches are indeed under compression. If the arch were under any considerable amount of tensile force anywhere besides the three hinges described above, it would have failed long ago. Another important observation to be made about the Ponte Fabricio is that the construction of the two arches creates cancelling thrust at the center pier. The opposing reactions at the right side of arch one and the left side of arch two illustrate that as weight tends to force the arches to “fold” outwards, the two work in harmony to hold each other up.

Ponte Garibaldi

In this comparison between the Ponte Garibaldi and the Ponte Fabricio, it is assumed that the Ponte Garibaldi behaves like a three-hinged arch and does not consist of reinforced concrete, even though it does consist of reinforcing materials after its renovation in 1959.
The following analysis was used assuming the dimensions listed below in Table 2 via site visit:

Table 2: Ponte Garibaldi Values

Height (m.) 7
Width (m.) 23
Arch Width (m.) 55
Span-to-Height Ratio 7.86

The same thrust analysis was performed as with the Ponte Fabricio to yield reactions in the y-direction of 11,700 kips in compression and reactions in the x-direction of 53,700 kips compression

Note: The forces in the x-direction differ from those in the y-direction in magnitude due to the fact that the lever arms about the keystone hinge are no longer equal.


In the case of the Ponte Girabaldi, the reaction force in the x-direction is nearly five times the reaction force in the y-direction. This drastic change in relative directional force is due to geometry alone. When the lever arm for the reaction in the x-direction is not equal in length to that of the y-direction, this is said to be a segmental arch. In other words, a segmental arch is an arch that subtends the semi-circular 180-degree shape (Arches: Brittanica, 2013). As the span of the arches increases relative to the height of the bridge itself, the horizontal thrust increases along with it. The conclusion drawn from this is that Romans often used semi-circular arches whenever possible as the geometry of these arches provides a greater amount of the thrust to transfer to the ground via abutment or foundation.

However, Romans did use the segmental arch in their bridge design in certain cases. One example is the construction of the ancient Roman Limyra Bridge. This bridge is 320 meters long made up of 26 separate segmental arches. Each segmental arch has a span-height ratio of 5.3:1 (Ancient Roman Bridges, 2013). This structure is currently buried by river sediments and is surrounded by greenhouses, and its exact construction date is unknown. Another Roman segmental arch bridge resides in Padua, Italy and is called the Ponte Corvo. This bridge has a span-to-rise ratio of 2.8-3.4 (Galliazzo, 1994), however, this bridge’s three remaining arches are partly buried and walled up. It was constructed around 1 or 2 AD (Galliazzo, 1994).

The fact that these two ancient Roman segmental bridges are no longer functional is more evidence as to why unreinforced concrete bridges perform higher when they are semi-circular in geometry. This fact could be why there is such little evidence of segmental arches in Roman construction history.

From the perspective of the Ponte Garibaldi, which has a span-to-rise ratio of 7.86 and was renovated in 1959 as a reinforced concrete span, it’s reasonable to assume that the Romans would have had trouble accomplishing an unreinforced arch bridge with those dimensions. An article of history regarding the transition from unreinforced concrete to reinforced concrete from the Delaware Department of Transportation states,

“As the structural advantages of reinforced concrete became apparent, the heavy, filled barrel was lightened into ribs. Spandrel walls were opened giving a lighter appearance and decreasing dead load. This enabled the concrete arch to become flatter and multi-centered with longer spans possible. Designers were no longer limited to the semi-circular or segmental arch form of the stone arch bridge.”
– (DelDot, 1991)

The construction of the Ponte Garibaldi supports this statement made by DelDOT in their reports analyzing concrete bridges. Comparing it with the likes of the previously attempted segmental arches in Roman history again supports the notion that the Romans, most likely, would have had difficulty constructing a bridge of that stature and durability. Therefore, they stuck with the design of the semi-circular arch, most likely, because they knew of its stability and reliance without reinforcement. For instance, the Ponte Garibaldi spans 120 meters with just two arches, which rises seven meters approximately. The Roman Limyra Bridge spanned 320 meters, yet it need 26 arches of support to accomplish this and its span-to-rise ratio of 5.3:1 pales in comparison to the Garibaldi’s 7.86.

So why is this relevant? The idea of this analysis is to show that the structural side of design can vary significantly. There is more than one way to accomplish the task that both the Ponte Garibaldi and the Ponte Fabricio do, which is to cross the Tiber to some degree. One bridge, the Garibaldi, utilizes reinforcing and can span a great distance at little arch height, while the other can accomplish the same thing with more material and higher arches. The rest of the design process is dependant on other alternative influences. Other factors of design are discussed herein.

Materials Design

A large part of a structure’s strength comes from the materials it’s made of, so it makes sense that choice of construction material is major component of design. The Romans constructed their arched bridges with materials, which would fall under the category of masonry. Cut or shaped stones (usually bricks or travertine) were generally used for the cover on the outside of faces of the bridge we can see (see Figure 4). This cover serves as a means of making the bridge more appealing to look at on the outside, giving the bridge I white facade. The brick or travertine was generally constructed and attached using a mortar mixture. In addition, large rounded stones, made of tuff, were used during the first few phases of construction, as they could be cut to the exact shape of the arch and fit together without the need of mortar as a binding agent (Brown, 2001). Cut stones were more commonly used as their controlled shape allowed for more contact at the interface of adjacent pieces. In figure 3 below, a mine where red tuff was excavated is seen. This type of tuff was used for aggregate in the Roman’s hydraulic cement.

Figure 3: Tuff mines in underground Rome. Pictured above is red tuff most commonly seen in hydraulic cement as aggregate (Photo By: Self, 2013)

Figure 4: The underside of Ponte Fibricio displaying remnants of travertine covering at the lower right base (Photo By: Self, 2013)

The interior structure of the bridge foundation was generally constructed using a concrete fill of tuff, a rock made of consolidated volcanic ash (Taylor 2002). Tuff is a heavy constructing material, used much by the Romans, utilized in the case of arch bridges due to its weight, cheapness, and ease of use. The Romans by means of mines, see figure 3, obtained tuff and would mix the resulting chunk of stone with a cementitious mixture of pozzolanic ash, lime, and water. The combination would create a compressively strong material after setting aside time to cure and let the chemical reaction take place. Because what the Romans were creating was essentially concrete, the mixture has increased its strength over many years past its construction, and the weakest these arched bridges would have been is when they were first constructed (strictly focusing on concrete strength). Vitruvius documented Roman construction, among many other topics, in his Ten Books on Architecture. In book two, he discusses much of how Roman engineers mixed concrete. He instructs a ratio of 1:3 for lime to pozzolans for buildings and 1:2 for structures underwater. Because the flooding nature of the Tiber River, it can be assumed that a ratio closer to 1:2 was used for the bridge similar to the Ponte Fibricio at its foundation (Morgan, 1914).

As stated above, masonry arches perform very well in compression and horribly in tension, so it behooves the bridge to add weight distributed over the top of the arch. Doing so prevents any tension from occurring within the arch itself, which prevents excessive cracking from occurring. Too much weight over the top, however, and the arch will fail in shear if it is not abutted strongly. This is the case for a triumphal arch, where there are no abutments to transfer force from the arch to the ground horizontally.

There are many different materials the Romans used to accomplish the feat of building a structure like the Ponte Fabricio, and the masonry building materials the Romans used are due largely to the location of these resources. As can be seen by the map in Figure 5 below, the major tuff mines where Romans drew many materials from are located not only near Rome, but actually in the city of Rome itself. Pozzolanic ash could also be obtained, volcanic ash in Figure 5, from these sites due to the fact that the ash is found layered with the red tuff so often used by Romans in their concrete. The fact that the useful product is so close lends itself to lower cost as the cost of transportation decreases with closer proximity. Roman concrete also becomes a more viable option at this point because the time it takes for the materials to be processed is greatly reduced, making it quicker to obtain materials when necessary. In addition, the nearby ingredients for rudimentary concrete made it more likely for the Romans to come across the invention of hydraulic cement as not one necessary ingredient was far at any point and time. Romans could have chosen to make their bridge foundations out of other materials such as wood, but because the necessary ingredients for concrete were so close, it was used as the building material of choice. Figure 5, below, illustrates the close proximity of ancient Roman building resources.

Figure 5: Map of building resources near Rome (Photo By: DeLaine J. 1997)

Construction Design

The construction of the arched bridges passing over the Tiber also displays some unique decisions to be made regarding design. Because the Romans had very little in machinery at the time of building structures such as the Ponte Fabricio, they had to find intelligent ways to design their bridges without falling prey to the force of the Tiber River.

The first step in building an ancient Roman bridge was to construct the abutments. This task was more easily done as the work was primarily accomplished on land. Large tuff stones were cut and put in place within the soil for the arch to rest on. After the abutments were installed, construction of the foundation and piers took place, the most difficult task. In spots around the Mediterranean it was common for rivers to be dry enough to build these elements directly without interference as if they were working on dry land, but the Tiber does not fall under this category. Instead, the Romans built objects called cofferdams, which served as watertight palisades to divert water around the desired locations of piers and foundations. The cofferdams, according to Vitruvius, V.12 in his Ten Books on Architecture, were built of two concentric circles of wood rods, which were held together by clay, which filled in the voids between rods (Brown 2001). The idea behind the cofferdams was that water would infiltrate the protected space, but it would also lose its dynamic impact on the construction space. One problem a cofferdam might cause is that the restriction of water into a tighter space would increase flow; essentially causing higher amounts of scour and swirl around the piers. To counteract this, some cofferdams were created to be long and come to a point in the face of the current. This technique helped to eliminate the effect of the water’s sudden change in direction by making it smoother. With the force of water out of the equation, the Romans could work freely. The progression shown in Figure 6 below gives an example of a typical arched bridge foundation construction and wooden arch support construction. Although this example is of a simple wooden span, the same process was used for arched bridges (Macaulay, 1974).

Depending on the surface conditions below, the Romans would begin constructing directly onto the rock or they would dig down to more suitable rock. From here, they would pour in their mixture of cement bonded by pozzolana, lime, and water to sink to the bottom of the formwork and push out the water within (Brown 2001). From here, they would wait for the mixture to finish reacting with the water and harden. This cementitious mixture, referred to as opus caementicium, was filled to the desired height of where the arch was to begin. This point on the pier is called the springing point. Upon curing of the mixture for both possible methods, exterior mortared brick or travertine was traditionally applied to the outside for finish (Taylor 2002).

The next phase of Roman bridge construction involved implementing the beginnings of the arch structures between piers. As seen in the analysis above regarding horizontal thrust lines, a great amount of force in generated by the self-weight of the building blocks for these arches. Because of this, the arches were either constructed all at the same time or the pier between consecutive arches was made overly wide to resist the force of the newly created arch. In order to raise the stonework to begin with the construction of the arches, boats/buoys were placed and tied together across the Tiber connecting at each pier so as to prevent them from floating downstream (Macaulay, 1974). The Romans would use these boats to have access from pier to pier while installing the temporary false work depicted below in Figures 6.2, 6.3, and 6.4.

Figure 6.1: Cofferdam used by the ancient Romans to divert river water from the Tiber (Illustration By: Macaulay, D. 1974)

Figure 6.2: Installment of the cofferdams with preparation of pier construction used temporary boat bridge as access (Illustration By: Macaulay, D. 1974)

Figure 6.3: Construction of pier begins as outside is covered with travertine (Illustration By: Macaulay, D. 1974)

Figure 6.4: Piers are complete and framework begins for either wooden span or arched masonry stones (Illustration By: Macaulay, D. 1974)

Upon completion of all of the false work, large stones of tuff were cut, placed, and fitted together directly above the wooden temporary arches to make the arch barrel for the span. Layers of stone were added vertically to create two outer laying walls called spandrels. These spandrels would support the opus caementicium fill (hydraulic cement and mined red tuff) placed inside or loose material such as rubble (Taylor, 2002). A road was then paved on top of the leveled bridge and parapets were constructed to prevent commuters from falling off the sides into the Tiber. As can be seen below in Figures 7.1 and 7.2, the Ponte Fabricio was constructed with a cementitious mixture containing red tuff (upper right corner of both Figures), black stone blocks made from tuff, and was covered in both travertine and brick at some point.

Figure 7.1: The Ponte Fabricio’s four different layers of material used (Photo By: Self, 2013)

Figure 7.2: A close-up of the red tuff cementitious mixture used to fill in the core of the Ponte Fabricio (Photo By: Self, 2013)

Overall, the construction methods used by the Romans to build these ancient bridges were a function of the environment and the technology they had at the time. Thus, the Romans illustrate that design must also take into account careful planning of your surroundings and building within the means of the technology at ones disposal.

A good example of this can be seen in the recent comparison between the Ponte Fabricio and the Ponte Garibaldi. The Ponte Garibaldi was constructed using reinforced concrete and can span a distance of 120 meters with merely a 7-meter height difference and two arches. The Ponte Fabricio spans 62 meters with a 14.5-meter height and two arches. Clearly, the advantageous geometry of the Ponte Garibaldi (as discussed in the analysis previously) stems from the fact that reinforced concrete wasn’t implemented as a construction technique until the late 1800’s. As Vitruvius claims in Book one Chapter one of his ten books on architecture, “He who is theoretical as well as practical, is therefore doubly armed; able not only to prove the propriety of his design, but equally so to carry it into execution.” Vitruvius simply explains that a grand design cannot be built if the means to build it are not within the scope of the project, as illustrated in the comparison between the Ponte Garibaldi and the Ponte Fabricio. The Ponte Fabricio could have been theorized like the Ponte Garibaldi, but lack of technology, therefore practicality eliminated that possibility. Technology is clearly a large factor of design capabilities for this reason.

Environmental Design

An important design element when planning where to construct a bridge lies within its intended environment. Much of where a bridge is located depends on the demand request of its environment. Rabun Taylor of Harvard University writes about the Tiber River and how ancient bridges helped the development of ancient Rome. He lists four main bridge functionalities:

1) Private Bridge: This type of bridge was less common and was clearly reserved for those who were wealthy enough to afford the materials and labor for construction. These bridges were placed near the owner’s property or near a location they wished to access more easily themselves. An example of this type of functionality is the Pons Agrippae.

2) Public Bridge: These bridges are the bridges, which are most commonly seen today. A bridge of this type covers the needs of getting workers to their respective jobs, helping worshippers get to their chapels, and distribution of food. The Ponte Fabricio is a great example of this type of bridge as it connects the mainland (today Campus Martius) to Tiber Island. Here, Romans could visit the Temple of Aesculapius, and today, can still access a hospital, which was founded in 1584 and still operates. A bridge like this would be placed in a location where the highest urban density existed as to accommodate the high demand of transport in that location.

3) Traffic Bridge: Helped serve as a relief for extra urban traffic, which came and went on the very busy consular highways. An example of this type of bridge is the Pons Sublicius. These bridges were also constructed in areas of high urban density to accommodate the large number of citizens wanting to utilize it.

4) Aqueduct Aiding Bridge: Essentially, this bridge helped aid in supporting the aqueducts enough to get into the city of Rome. The only example of this type of bridge is the Pons Traiani, which is very little documented.
– (Taylor, 2002)

These four needs were inflated as the Roman market grew and the city grew into a strong world power and market holder. With control over the Tiber River and tolls for crossing it by both bridge and ferry, the Romans saw potential in bridge building after the success of the Pons Sublicius. The success of this bridge in bringing salt over the river and making transportation over the Tiber easy caused economic growth in Rome’s center (Taylor, 2002). As a result, the Pons Aemilius was constructed to help control the high demand of crossing the Tiber and begin growing Rome into a network of transportation. The history of these two bridges show urban expansion can create a need for additional access points over a river, and hence, can trigger the design of a new bridge. This expansion of Rome can even be seen today as over twenty pedestrian and traffic bridges currently cross the Tiber easily within Rome city limits. Figure 8 below displays the dense distribution of bridges within the heart of Rome, as seen in yellow, caused by the high demand of foot and automobile traffic across the Tiber.